A weighted mean (or weighted average) is like an ordinary mean, but the observations don't contribute equally - more emphasis is placed on some data values than others; they are weighted by a bigger or smaller amount than 1/n.

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Compare Log-Normal Distributions

I am looking at distributions for the fuel consumption of vehicles in the US and I have two sets of data: Data Set 1 - This is a dataset for the fuel consumption of all vehicles made available for ...
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Weighted average of measurements with unequal errors

Suppose I have the numbers below. Consider them as results of some measurement. ...
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7 views

Appropriate weighting for averages

What is the appropriate (or the advantages of disadvantages for each) measure for weighting mortality rates across countries: total population or total number of deaths? For example, if you have ...
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26 views

Contribution of group to difference in total measurement

Say we have a response (0 1) of success and we measure the percentage of success in two years. We observe an increase in the percentage of success. The population (different in two years) is divided ...
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Weighted Standard Deviation vs. Weighted Regression Standard Error

This is an R question. I have $n$ observations of the variable $y$, with each observation, $i$, weighted by $w(i)$. Each $w(i)$ weight falls between zero and 1, with the sum of the weights, ...
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How to bootstrap confidence of a weighted measure?

I have a large data set of 20M observations with 20+ measures for each observation (people). Additionally I have a set of weights that reflect the racial population where each person lives. For ...
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Estimated Treatment Effect in the full sample is not between the estimates of the stratified samples?

I am estimating the relationship between students' math scores and using a supplemental math software. I've adjusted for some demographic variables in the model. In my first model, I use the full ...
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How to symmetrically adjust data by removing certain value

Say I have a data set in the following format: {a:200, b: 100; c:400} The sum of a, b and c equals 700. Now, I have another value which is supposed to be the actual total say 500. How do I adjust ...
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Computationally cheap estimation of the mode from 2D samples

I say 'mode' in the title – perhaps there's something more appropriate I can find. Here's my problem: A person is in a $100\mathrm m$ by $500\mathrm m$ space. I have about 100 samples randomly ...
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Aggregating based on inverse probability weight

I have a data set that includes life quality indices for many cities. I want to aggregate the indices to the metropolitan level. Since some cities in each metro area are missing, the data set provides ...
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How do I determine the appropriate “weight” of a point in fantasy basketball?

For fantasy basketball, I want to quantify a player's output based on his Points, Rebounds, Assists, Steals, 3s, and Blocks production. Let's pretend that over the course of an imaginary basketball ...
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130 views

Hypothesis test for difference between domain means with weighted data

I have a large dataset that is weighted due to: probability proportional to size sampling, & disproportionate stratification. I would like to compare the means for two different domains ...
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How do I determine the significance of a difference in weighted averages from a Likert-type survey question?

I have multiple survey questions that give respondents 4 Likert-type options for a response to qualify their knowledge/skill in a particular area. I have calculated a weighted average (and divided by ...
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Number of occurrences gives higher weights

I have this algorithm that I'm implementing that I need to change to give it a better accuracy. To give you an idea of the problem, I have a a bunch of lists that contain items and all items in these ...
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Paired test: many repetitions, few subjects

I have a situation similar to this: 9 normal-sighted subjects are each tested under two conditions: say, with and without spectacles (of a fixed power) and asked to reach towards an object many times ...
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how to use global weights to update local ones

I have a population of data points. Each data point expresses a different name. Each such name belongs to a different ethnicity, say {A, B, C, D, E}, with a probability. The sum of probabilities for a ...
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Average difference in averages and t-test

I'm currently working with some individual level data and have run up against a wall in figuring out the best way to analyse it. Let me describe: We have a sample of N=9000 Physicians. For each ...
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Calculate scores for users with varying activity

I have a web application which allows users to take questions. Ultimately I store the following data: 1) Questions attempted by each user 2) Questions correct by each user 3) Avg. Time per user for ...
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How to use global weights when normalizing a mean value?

This is a very silly question, however, it confuses me a lot! Let's suppose that each observation consists of the prob of $A$ and the prob of $B$, with values $1/2$ and $1/2$ respectively. Also, ...
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League table with weighted result

I have a simple set of data indicating completion rates that I want to present as a ranked/league table. The data available is that for every visit of a person, a plan document should be completed by ...
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81 views

Averaging across independent strata: confidence interval

I've $k$ independent strata, with populations $n_1,\dots,n_k$, and have estimated the mean in each stratum $\bar{x_1}, \dots \bar{x_k}$ and obtained the standard errors $se_1,\dots,se_k$ (using STATA ...
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Best fit of weighted mean?

The title might be somewhat misleading. I am trying to solve the following optimization problem and do not find any clues. Can any one help? I have a sequence of $n$ observation $s_i$. Each ...
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Weighting datapoints by uncertainty - asymmetric CIs

I have several estimates obtained using different softwares, these programs give me an estimate as well as a 95% confidence interval. However, these CIs are not symmetric around my point estimates, ...